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    "## 目录\n",
    "\n",
    "- 感知机分类器\n",
    "- 逻辑回归分类器\n",
    "- 图像分类数据集\n",
    "- softmax回归的从零开始实现\n",
    "- softmax回归的简洁实现"
   ]
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   "id": "412d121a-f1f9-4150-ad97-39c5b0edc498",
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   "source": [
    "## 感知机分类器"
   ]
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    "Perceptron是一个线性分类器。它的工作方式与没有隐藏层的神经网络相同（只有输入和输出）。\n",
    "\n",
    "![perceptron](perceptron.png)\n",
    "\n",
    "首先，它对给定的数据集进行权重训练，然后通过网络对一个新项目进行分类。\n",
    "\n",
    "> 注意，在分类问题中，每个节点代表一个类别。最终的分类是具有最大输出值的类/节点。"
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    "### 实现\n",
    "\n",
    "`PerceptionLinearLearner` 用于训练（计算）给定数据集的权重。\n",
    "\n",
    "函数`predict`用于对一个新的项目进行分类：该函数计算项目与外层每个节点的计算权重的（代数）点积。然后，它选择一个最大的值，将项目归入相应的类别。"
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       "<h2></h2>\n",
       "\n",
       "<div class=\"highlight\"><pre><span></span><span class=\"k\">class</span> <span class=\"nc\">PerceptionLinearLearner</span><span class=\"p\">(</span><span class=\"n\">LinearClassifier</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">    </span><span class=\"sd\">&quot;&quot;&quot;</span>\n",
       "<span class=\"sd\">    Perception linear classifier: hard threshold</span>\n",
       "<span class=\"sd\">    &quot;&quot;&quot;</span>\n",
       "    <span class=\"k\">def</span> <span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">dataset</span><span class=\"p\">,</span> <span class=\"n\">learning_rate</span><span class=\"o\">=</span><span class=\"mf\">0.01</span><span class=\"p\">,</span> <span class=\"n\">epochs</span><span class=\"o\">=</span><span class=\"mi\">100</span><span class=\"p\">):</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">idx_i</span> <span class=\"o\">=</span> <span class=\"n\">dataset</span><span class=\"o\">.</span><span class=\"n\">inputs</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">idx_t</span> <span class=\"o\">=</span> <span class=\"n\">dataset</span><span class=\"o\">.</span><span class=\"n\">target</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">examples</span> <span class=\"o\">=</span> <span class=\"n\">dataset</span><span class=\"o\">.</span><span class=\"n\">examples</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">num_examples</span> <span class=\"o\">=</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">examples</span><span class=\"p\">)</span>\n",
       "        <span class=\"c1\"># initialize random weights</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">w</span> <span class=\"o\">=</span> <span class=\"n\">random_weights</span><span class=\"p\">(</span><span class=\"n\">min_value</span><span class=\"o\">=-</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"n\">num_weights</span><span class=\"o\">=</span><span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">idx_i</span><span class=\"p\">)</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "        <span class=\"c1\"># learning loop</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">learn</span><span class=\"p\">(</span><span class=\"n\">learning_rate</span><span class=\"p\">,</span> <span class=\"n\">epochs</span><span class=\"p\">)</span>\n",
       "        \n",
       "    <span class=\"k\">def</span> <span class=\"nf\">learn</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">learning_rate</span><span class=\"p\">,</span> <span class=\"n\">epochs</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">        </span><span class=\"sd\">&quot;&quot;&quot; learning loop &quot;&quot;&quot;</span>\n",
       "        <span class=\"k\">def</span> <span class=\"nf\">loss</span><span class=\"p\">(</span><span class=\"n\">example</span><span class=\"p\">,</span> <span class=\"n\">w</span><span class=\"p\">,</span> <span class=\"n\">idx_i</span><span class=\"p\">,</span> <span class=\"n\">idx_t</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">            </span><span class=\"sd\">&quot;&quot;&quot; error: difference between estimation and true value &quot;&quot;&quot;</span>\n",
       "            <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
       "        \n",
       "        <span class=\"k\">def</span> <span class=\"nf\">update</span><span class=\"p\">(</span><span class=\"n\">w</span><span class=\"p\">,</span> <span class=\"n\">learning_rate</span><span class=\"p\">,</span> <span class=\"n\">err</span><span class=\"p\">,</span> <span class=\"n\">X_col</span><span class=\"p\">,</span> <span class=\"n\">num_examples</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">            </span><span class=\"sd\">&quot;&quot;&quot; update weights &quot;&quot;&quot;</span>\n",
       "            <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
       "\n",
       "        <span class=\"k\">def</span> <span class=\"nf\">homogeneous</span><span class=\"p\">(</span><span class=\"n\">num_examples</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">            </span><span class=\"sd\">&quot;&quot;&quot; build homogeneous coordinates &quot;&quot;&quot;</span>\n",
       "            <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
       "\n",
       "        <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
       "\n",
       "    <span class=\"k\">def</span> <span class=\"nf\">predict</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">        </span><span class=\"sd\">&quot;&quot;&quot; make prediction &quot;&quot;&quot;</span>\n",
       "        <span class=\"k\">return</span> <span class=\"nb\">int</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">dot</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">w</span><span class=\"p\">,</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">x</span><span class=\"p\">))</span>\n",
       "</pre></div>\n",
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   "source": [
    "import sys\n",
    "sys.path.insert(1, '../')\n",
    "from utils.dataset4learners import *\n",
    "from LinearClassifier_3 import *\n",
    "\n",
    "psource(PerceptionLinearLearner)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c4fac32-dfa4-46d4-a2c4-8e5724f1def3",
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   "source": [
    "#### 实现要点\n",
    "\n",
    "```py\n",
    "def learn(self, learning_rate, epochs):\n",
    "    \"\"\" learning loop \"\"\"\n",
    "    def loss(example, w, idx_i, idx_t):\n",
    "        \"\"\" error: difference between estimation and true value \"\"\"\n",
    "        x = example的齐次坐标表示\n",
    "        y = w * x，即预测值\n",
    "        t = 真实值\n",
    "        return y - t\n",
    "\n",
    "    def update(w, learning_rate, err, X_col, num_examples):\n",
    "        \"\"\" update weights \"\"\"\n",
    "        遍历w[i]:\n",
    "            w[i] = w[i] - 学习率 * 误差值 * 自变量X[i] / 样本数量)\n",
    "\n",
    "    def homogeneous(num_examples):\n",
    "        \"\"\" build homogeneous coordinates \"\"\"\n",
    "        return 齐次坐标表示\n",
    "\n",
    "    X_col = 齐次坐标表示\n",
    "    for epoch in range(epochs):\n",
    "        err = []\n",
    "        # pass over all examples\n",
    "        for example in self.examples:\n",
    "            err.append(loss(example, w, idx_i, idx_t))\n",
    "\n",
    "        # update weights\n",
    "        update(w, 学习率, err, X_col, 样本数量)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8f78b41-5136-4563-8359-67c1dae52642",
   "metadata": {},
   "source": [
    "> 注意，Perceptron是一个单层的神经网络，在后面课程中讲授。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca1d7196-b054-4718-9402-c0a377fc53a6",
   "metadata": {},
   "source": [
    "### 例子\n",
    "\n",
    "我们将在`iris`数据集上训练感知机。\n",
    "\n",
    "尽管`BackPropagationLearner`使用的是整数索引而不是字符串，我们需要将类名转换成整数。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c37147ed-40e7-4b05-83e3-5c4db4c0a039",
   "metadata": {
    "tags": []
   },
   "source": [
    "```py\n",
    "iris = DataSet(name=\"iris\")\n",
    "iris.classes_to_numbers()\n",
    "\n",
    "perceptron = PerceptionLinearLearner(iris)\n",
    "print(perceptron.predict([5, 3, 1, 0.1]))\n",
    "```"
   ]
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  {
   "cell_type": "markdown",
   "id": "debca21b-5262-49ac-8502-8e692e9d26af",
   "metadata": {},
   "source": [
    "正确的输出是0，这意味着该物品属于第一类，\"setosa\"。注意Perceptron算法并不完美，可能会产生错误的分类。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6ab0a90-bf04-497b-9795-31e62155054d",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 逻辑回归分类器"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55e14e99-4e16-4ef2-a652-43a51364c144",
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   "source": [
    "逻辑回归将感知机采用的硬性阈值函数改为柔性阈值，可以更好地对分界区域的不确定性建模。\n",
    "\n",
    "### 实现\n"
   ]
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       "<body>\n",
       "<h2></h2>\n",
       "\n",
       "<div class=\"highlight\"><pre><span></span><span class=\"k\">class</span> <span class=\"nc\">LogisticLinearLeaner</span><span class=\"p\">(</span><span class=\"n\">LinearClassifier</span><span class=\"p\">):</span>\n",
       "    <span class=\"k\">def</span> <span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">dataset</span><span class=\"p\">,</span> <span class=\"n\">learning_rate</span><span class=\"o\">=</span><span class=\"mf\">0.01</span><span class=\"p\">,</span> <span class=\"n\">epochs</span><span class=\"o\">=</span><span class=\"mi\">100</span><span class=\"p\">):</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">idx_i</span> <span class=\"o\">=</span> <span class=\"n\">dataset</span><span class=\"o\">.</span><span class=\"n\">inputs</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">idx_t</span> <span class=\"o\">=</span> <span class=\"n\">dataset</span><span class=\"o\">.</span><span class=\"n\">target</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">examples</span> <span class=\"o\">=</span> <span class=\"n\">dataset</span><span class=\"o\">.</span><span class=\"n\">examples</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">num_examples</span> <span class=\"o\">=</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">examples</span><span class=\"p\">)</span>\n",
       "        <span class=\"c1\"># initialize random weights</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">w</span> <span class=\"o\">=</span> <span class=\"n\">random_weights</span><span class=\"p\">(</span><span class=\"n\">min_value</span><span class=\"o\">=-</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"n\">num_weights</span><span class=\"o\">=</span><span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">idx_i</span><span class=\"p\">)</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "        <span class=\"c1\"># learning loop</span>\n",
       "        <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">learn</span><span class=\"p\">(</span><span class=\"n\">learning_rate</span><span class=\"p\">,</span> <span class=\"n\">epochs</span><span class=\"p\">)</span>\n",
       "        \n",
       "    <span class=\"k\">def</span> <span class=\"nf\">learn</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">learning_rate</span><span class=\"p\">,</span> <span class=\"n\">epochs</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">        </span><span class=\"sd\">&quot;&quot;&quot; learning loop &quot;&quot;&quot;</span>\n",
       "        <span class=\"k\">def</span> <span class=\"nf\">loss</span><span class=\"p\">(</span><span class=\"n\">example</span><span class=\"p\">,</span> <span class=\"n\">w</span><span class=\"p\">,</span> <span class=\"n\">idx_i</span><span class=\"p\">,</span> <span class=\"n\">idx_t</span><span class=\"p\">,</span> <span class=\"n\">h</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">            </span><span class=\"sd\">&quot;&quot;&quot; error: difference between estimation and true value &quot;&quot;&quot;</span>\n",
       "            <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
       "        \n",
       "        <span class=\"k\">def</span> <span class=\"nf\">update</span><span class=\"p\">(</span><span class=\"n\">w</span><span class=\"p\">,</span> <span class=\"n\">learning_rate</span><span class=\"p\">,</span> <span class=\"n\">err</span><span class=\"p\">,</span> <span class=\"n\">h</span><span class=\"p\">,</span> <span class=\"n\">X_col</span><span class=\"p\">,</span> <span class=\"n\">num_examples</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">            </span><span class=\"sd\">&quot;&quot;&quot; update weights &quot;&quot;&quot;</span>\n",
       "            <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
       "\n",
       "        <span class=\"k\">def</span> <span class=\"nf\">homogeneous</span><span class=\"p\">(</span><span class=\"n\">num_examples</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">            </span><span class=\"sd\">&quot;&quot;&quot; build homogeneous coordinates &quot;&quot;&quot;</span>\n",
       "            <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
       "\n",
       "        <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
       "\n",
       "    <span class=\"k\">def</span> <span class=\"nf\">predict</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n",
       "<span class=\"w\">        </span><span class=\"sd\">&quot;&quot;&quot; make prediction &quot;&quot;&quot;</span>\n",
       "        <span class=\"k\">return</span> <span class=\"nb\">int</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">dot</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">w</span><span class=\"p\">,</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">x</span><span class=\"p\">))</span>\n",
       "</pre></div>\n",
       "</body>\n",
       "</html>\n"
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   "source": [
    "psource(LogisticLinearLeaner)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64d23b34-7203-4abe-bb3b-b3e65f192d62",
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   "source": [
    "#### 实现要点\n",
    "\n",
    "```py\n",
    "def learn(self, learning_rate, epochs):\n",
    "    \"\"\" learning loop \"\"\"\n",
    "    def loss(example, w, idx_i, idx_t, h):\n",
    "        \"\"\" error: difference between estimation and true value \"\"\"\n",
    "        x = example的齐次坐标表示\n",
    "        y = Sigmoid(w * x)，即预测值\n",
    "        h.append(Sigmoid().derivative(y))：收集梯度值\n",
    "        t = 真实值\n",
    "        return y - t\n",
    "\n",
    "    def update(w, learning_rate, err, h, X_col, num_examples):\n",
    "        \"\"\" update weights \"\"\"\n",
    "        遍历w[i]:\n",
    "            w[i] = w[i] - 学习率 * 误差值err[i] * 梯度值h[i] / 样本数量)\n",
    "\n",
    "    def homogeneous(num_examples):\n",
    "        \"\"\" build homogeneous coordinates \"\"\"\n",
    "        同感知机\n",
    "\n",
    "    同感知机\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34dde5da-d093-4021-ae8b-7a38cd5b11dc",
   "metadata": {},
   "source": [
    "该算法首先为输入变量分配一些随机权重，然后根据计算的误差更新每个变量的权重。最后用更新后的权重进行预测。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b3f1358-fe11-4499-8fc1-f8a7fb6ef826",
   "metadata": {
    "tags": []
   },
   "source": [
    "```py\n",
    "iris = DataSet(name=\"iris\")\n",
    "iris.classes_to_numbers()\n",
    "\n",
    "logisticer = LogisticLinearLeaner(iris)\n",
    "print(logisticer.predict([5, 3, 1, 0.1]))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0e066c5-554b-4286-ae5f-1f71dd7b95a8",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": []
   },
   "source": [
    "## 图像分类数据集"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19b612e3-6ede-4ffa-a9dd-14a0480a2c8f",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "MNIST数据集是图像分类中广泛使用的数据集之一，但作为基准数据集过于简单。\n",
    "\n",
    "我们将使用类似但更复杂的Fashion-MNIST数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "451140a0-6c93-45e0-8e19-8ffb51099e77",
   "metadata": {
    "origin_pos": 2,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "import torchvision\n",
    "from torch.utils import data\n",
    "from torchvision import transforms\n",
    "from d2l import torch as d2l\n",
    "\n",
    "d2l.use_svg_display()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5386450-4cdd-4c05-9524-25505b67f22c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "通过框架中的内置函数将Fashion-MNIST数据集下载并读取到内存中"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "af7b66a6-a2ca-4ec3-981e-8acaf5880cbe",
   "metadata": {
    "origin_pos": 9,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz\n",
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz to ../data/FashionMNIST/raw/train-images-idx3-ubyte.gz\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100.0%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ../data/FashionMNIST/raw/train-images-idx3-ubyte.gz to ../data/FashionMNIST/raw\n",
      "\n",
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz\n",
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz to ../data/FashionMNIST/raw/train-labels-idx1-ubyte.gz\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100.0%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ../data/FashionMNIST/raw/train-labels-idx1-ubyte.gz to ../data/FashionMNIST/raw\n",
      "\n",
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz\n",
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz to ../data/FashionMNIST/raw/t10k-images-idx3-ubyte.gz\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100.0%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ../data/FashionMNIST/raw/t10k-images-idx3-ubyte.gz to ../data/FashionMNIST/raw\n",
      "\n",
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz\n",
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz to ../data/FashionMNIST/raw/t10k-labels-idx1-ubyte.gz\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100.0%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ../data/FashionMNIST/raw/t10k-labels-idx1-ubyte.gz to ../data/FashionMNIST/raw\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(60000, 10000)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 通过ToTensor实例将图像数据从PIL类型变换成32位浮点数格式，\n",
    "# 并除以255使得所有像素的数值均在0到1之间\n",
    "trans = transforms.ToTensor()\n",
    "mnist_train = torchvision.datasets.FashionMNIST(\n",
    "    root=\"../data\", train=True, transform=trans, download=True)\n",
    "mnist_test = torchvision.datasets.FashionMNIST(\n",
    "    root=\"../data\", train=False, transform=trans, download=True)\n",
    "\n",
    "len(mnist_train), len(mnist_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e5de50d6-1fe0-407d-87a9-8eec3c6c475d",
   "metadata": {
    "origin_pos": 12,
    "tab": [
     "pytorch"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 28, 28])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist_train[0][0].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87d0348b-ec5d-4299-9d8c-08987de460f1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "两个可视化数据集的函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0557638e-71b8-40ce-95e6-5d61038f1ffc",
   "metadata": {
    "origin_pos": 17,
    "tab": [
     "pytorch"
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   "outputs": [],
   "source": [
    "def get_fashion_mnist_labels(labels):  \n",
    "    \"\"\"返回Fashion-MNIST数据集的文本标签\"\"\"\n",
    "    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',\n",
    "                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']\n",
    "    return [text_labels[int(i)] for i in labels]\n",
    "\n",
    "def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):  \n",
    "    \"\"\"绘制图像列表\"\"\"\n",
    "    figsize = (num_cols * scale, num_rows * scale)\n",
    "    _, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize)\n",
    "    axes = axes.flatten()\n",
    "    for i, (ax, img) in enumerate(zip(axes, imgs)):\n",
    "        if torch.is_tensor(img):\n",
    "            ax.imshow(img.numpy())  # 图片张量\n",
    "        else:\n",
    "            ax.imshow(img)  # PIL图片\n",
    "        ax.axes.get_xaxis().set_visible(False)\n",
    "        ax.axes.get_yaxis().set_visible(False)\n",
    "        if titles:\n",
    "            ax.set_title(titles[i])\n",
    "    return axes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c9255c0-c447-4232-a1e8-9cbdd63f2a62",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "几个样本的图像及其相应的标签"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6bd5a31f-a289-4ab2-9ee5-bbe8322ac216",
   "metadata": {
    "origin_pos": 20,
    "tab": [
     "pytorch"
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   },
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = next(iter(data.DataLoader(mnist_train, batch_size=18)))\n",
    "show_images(X.reshape(18, 28, 28), 2, 9, titles=get_fashion_mnist_labels(y));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ce47a48-d8e3-46a6-8e2b-009c4e299341",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "读取一小批量数据，大小为`batch_size`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b15b88d6-d561-4971-9c20-b30d2618da04",
   "metadata": {
    "origin_pos": 27,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'20.21 sec'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "batch_size = 256\n",
    "\n",
    "def get_dataloader_workers():  \n",
    "    \"\"\"使用4个进程来读取数据\"\"\"\n",
    "    return 4\n",
    "\n",
    "train_iter = data.DataLoader(mnist_train, batch_size, shuffle=True,\n",
    "                             num_workers=get_dataloader_workers())\n",
    "\n",
    "timer = d2l.Timer()\n",
    "for X, y in train_iter:\n",
    "    continue\n",
    "f'{timer.stop():.2f} sec'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e0a3486-8788-4a87-b9b9-cb327ba7d2ca",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "定义`load_data_fashion_mnist`函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5f88e2a1-88b6-49c3-a8b8-2ac9602a71a8",
   "metadata": {
    "origin_pos": 33,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def load_data_fashion_mnist(batch_size, resize=None):  \n",
    "    \"\"\"下载Fashion-MNIST数据集，然后将其加载到内存中\"\"\"\n",
    "    trans = [transforms.ToTensor()]\n",
    "    if resize:\n",
    "        trans.insert(0, transforms.Resize(resize))\n",
    "    trans = transforms.Compose(trans)\n",
    "    mnist_train = torchvision.datasets.FashionMNIST(\n",
    "        root=\"../data\", train=True, transform=trans, download=True)\n",
    "    mnist_test = torchvision.datasets.FashionMNIST(\n",
    "        root=\"../data\", train=False, transform=trans, download=True)\n",
    "    return (data.DataLoader(mnist_train, batch_size, shuffle=True,\n",
    "                            num_workers=get_dataloader_workers()),\n",
    "            data.DataLoader(mnist_test, batch_size, shuffle=False,\n",
    "                            num_workers=get_dataloader_workers()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b60ce5c6-c1e3-4d51-9d2a-d35e114773ed",
   "metadata": {
    "origin_pos": 33,
    "slideshow": {
     "slide_type": "slide"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([32, 1, 64, 64]) torch.float32 torch.Size([32]) torch.int64\n"
     ]
    }
   ],
   "source": [
    "train_iter, test_iter = load_data_fashion_mnist(32, resize=64)\n",
    "for X, y in train_iter:\n",
    "    print(X.shape, X.dtype, y.shape, y.dtype)\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b3bc703-261c-4f28-8b13-10599cdfb648",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": []
   },
   "source": [
    "## softmax回归的从零开始实现"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "461c158e-d492-4138-a1dc-a6dee27856c3",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "就像我们从零开始实现线性回归一样，你应该知道实现softmax回归的细节"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7c6ea6a5-00d4-4032-8b69-a23295a1c3b3",
   "metadata": {
    "origin_pos": 4,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from IPython import display\n",
    "from d2l import torch as d2l\n",
    "\n",
    "batch_size = 256\n",
    "train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79517ad9-cddb-4ee2-9f61-43e0b6bb3341",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "将展平每个图像，把它们看作长度为784的向量。\n",
    "因为我们的数据集有10个类别，所以网络输出维度为10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bf6ec527-910e-42ce-b24c-c72da6fa9c74",
   "metadata": {
    "origin_pos": 7,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "num_inputs = 784\n",
    "num_outputs = 10\n",
    "\n",
    "W = torch.normal(0, 0.01, size=(num_inputs, num_outputs), requires_grad=True)\n",
    "b = torch.zeros(num_outputs, requires_grad=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2499dc12-833a-4851-b5de-859d86f428c5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "给定一个矩阵`X`，我们可以对所有元素求和"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e7fbccdf-9d88-4244-963a-33ebe05ba5ae",
   "metadata": {
    "origin_pos": 10,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[5., 7., 9.]]),\n",
       " tensor([[ 6.],\n",
       "         [15.]]))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])\n",
    "X.sum(0, keepdim=True), X.sum(1, keepdim=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7338e047-94ed-438d-a0b0-2477692b0c45",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "实现softmax\n",
    "\n",
    "$$\n",
    "\\mathrm{softmax}(\\mathbf{X})_{ij} = \\frac{\\exp(\\mathbf{X}_{ij})}{\\sum_k \\exp(\\mathbf{X}_{ik})}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "073aadb5-9a24-44e3-ac4b-3bae84a3a9e2",
   "metadata": {
    "origin_pos": 14,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def softmax(X):\n",
    "    X_exp = torch.exp(X)\n",
    "    partition = X_exp.sum(1, keepdim=True)\n",
    "    return X_exp / partition # 广播机制"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17706f99-24f6-446f-9f4a-a17368170e3f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "我们将每个元素变成一个非负数。\n",
    "此外，依据概率原理，每行总和为1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2ff371fa-6e82-4540-8c7d-0bba75225e1f",
   "metadata": {
    "origin_pos": 16,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[0.3532, 0.0347, 0.0805, 0.0395, 0.4921],\n",
       "         [0.6108, 0.0814, 0.1468, 0.0484, 0.1126]]),\n",
       " tensor([1., 1.]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.normal(0, 1, (2, 5))\n",
    "X_prob = softmax(X)\n",
    "X_prob, X_prob.sum(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02ba4bf7-0785-4958-afbf-9519f33ed8af",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "实现softmax回归模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ec1c7adf-b253-48cb-8abc-395098c3635e",
   "metadata": {
    "origin_pos": 19,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def net(X):\n",
    "    return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1ee288d-3e6e-41de-b4f5-c020e83bd14e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "创建一个数据样本`y_hat`，其中包含2个样本在3个类别的预测概率，\n",
    "以及它们对应的标签`y`。\n",
    "使用`y`作为`y_hat`中概率的索引"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "83632ade-00af-4692-887f-cd13041c814d",
   "metadata": {
    "origin_pos": 21,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1000, 0.5000])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = torch.tensor([0, 2]) # 在第二个样本中，第三类是正确的预测\n",
    "y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])\n",
    "y_hat[[0, 1], y] # 使用y作为y_hat中概率的索引"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c40efbc6-376d-4557-8b46-35c6aff4f979",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "实现交叉熵损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f070bea1-2b36-402e-828f-29d2446b0c56",
   "metadata": {
    "origin_pos": 24,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2.3026, 0.6931])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def cross_entropy(y_hat, y):\n",
    "    \"\"\" 避免低效的for循环 \"\"\"\n",
    "    return - torch.log(y_hat[range(len(y_hat)), y])\n",
    "\n",
    "cross_entropy(y_hat, y) # 损失函数，越低越好"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9374a06e-27ed-42fa-a1c9-0c6d90dd4a48",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "将预测类别与真实`y`元素进行比较"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "97a56aa3-f780-4f32-98ca-086d6e1024f0",
   "metadata": {
    "origin_pos": 29,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def accuracy(y_hat, y):  \n",
    "    \"\"\"计算预测正确的数量\"\"\"\n",
    "    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:\n",
    "        y_hat = y_hat.argmax(axis=1)\n",
    "    cmp = y_hat.type(y.dtype) == y # 数据类型转成一致\n",
    "    return float(cmp.type(y.dtype).sum())\n",
    "\n",
    "accuracy(y_hat, y) / len(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "585af5a4-d317-42ee-a5f1-255a594856fa",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "我们可以评估在任意模型`net`的精度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "540c6f10-7592-4fd3-8221-0ef56f88a0bf",
   "metadata": {
    "origin_pos": 32,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def evaluate_accuracy(net, data_iter):  \n",
    "    \"\"\"计算在指定数据集上模型的精度\"\"\"\n",
    "    if isinstance(net, torch.nn.Module):\n",
    "        net.eval()  # 将模型设置为评估模式\n",
    "    metric = Accumulator(2)  # 正确预测数、预测总数\n",
    "    with torch.no_grad():\n",
    "        for X, y in data_iter:\n",
    "            metric.add(accuracy(net(X), y), y.numel())\n",
    "    return metric[0] / metric[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7593436-0ca0-4fc3-ae2c-7d7311ddb9f6",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "`Accumulator`实例中创建了2个变量，\n",
    "分别用于存储正确预测的数量和预测的总数量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "bb38e91c-b8aa-4912-862e-9080a0bbda66",
   "metadata": {
    "origin_pos": 36,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1004"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class Accumulator:  \n",
    "    \"\"\"在n个变量上累加\"\"\"\n",
    "    def __init__(self, n):\n",
    "        self.data = [0.0] * n\n",
    "\n",
    "    def add(self, *args):\n",
    "        self.data = [a + float(b) for a, b in zip(self.data, args)]\n",
    "\n",
    "    def reset(self):\n",
    "        self.data = [0.0] * len(self.data)\n",
    "\n",
    "    def __getitem__(self, idx):\n",
    "        return self.data[idx]\n",
    "\n",
    "evaluate_accuracy(net, test_iter) # 随机权重初始化，随机猜测应该接近0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ca7e9be-2270-481f-b0c9-882b79efed78",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Softmax回归的训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c4c903ea-72eb-49a9-9888-8e8d5fd6f8a6",
   "metadata": {
    "origin_pos": 39,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def train_epoch_ch3(net, train_iter, loss, updater):  \n",
    "    \"\"\"训练模型一个迭代周期（定义见第3章）\"\"\"\n",
    "    if isinstance(net, torch.nn.Module):\n",
    "        net.train()  # 将模型设置为训练模式\n",
    "    metric = Accumulator(3)  # 训练损失总和、训练准确度总和、样本数\n",
    "    for X, y in train_iter:\n",
    "        # 计算梯度并更新参数\n",
    "        y_hat = net(X)\n",
    "        l = loss(y_hat, y)\n",
    "        if isinstance(updater, torch.optim.Optimizer):\n",
    "            # 使用PyTorch内置的优化器和损失函数\n",
    "            updater.zero_grad()\n",
    "            l.mean().backward()\n",
    "            updater.step()\n",
    "        else:  # 使用定制的优化器和损失函数\n",
    "            l.sum().backward()\n",
    "            updater(X.shape[0])\n",
    "        metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())\n",
    "    # 返回训练损失和训练精度\n",
    "    return metric[0] / metric[2], metric[1] / metric[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd06ef05-3914-4ecd-ba5e-59c4fea740c0",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "定义一个在动画中绘制数据的实用程序类"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3ecf8ca6-1797-497d-abc3-867a591bf464",
   "metadata": {
    "origin_pos": 42,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class Animator:  \n",
    "    \"\"\"在动画中绘制数据\"\"\"\n",
    "    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,\n",
    "                 ylim=None, xscale='linear', yscale='linear',\n",
    "                 fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,\n",
    "                 figsize=(3.5, 2.5)):\n",
    "        if legend is None:\n",
    "            legend = [] # 增量地绘制多条线\n",
    "        d2l.use_svg_display()\n",
    "        self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)\n",
    "        if nrows * ncols == 1:\n",
    "            self.axes = [self.axes, ]\n",
    "        # 使用lambda函数捕获参数\n",
    "        self.config_axes = lambda: d2l.set_axes(\n",
    "            self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)\n",
    "        self.X, self.Y, self.fmts = None, None, fmts\n",
    "\n",
    "    def add(self, x, y):\n",
    "        # 向图表中添加多个数据点\n",
    "        if not hasattr(y, \"__len__\"):\n",
    "            y = [y]\n",
    "        n = len(y)\n",
    "        if not hasattr(x, \"__len__\"):\n",
    "            x = [x] * n\n",
    "        if not self.X:\n",
    "            self.X = [[] for _ in range(n)]\n",
    "        if not self.Y:\n",
    "            self.Y = [[] for _ in range(n)]\n",
    "        for i, (a, b) in enumerate(zip(x, y)):\n",
    "            if a is not None and b is not None:\n",
    "                self.X[i].append(a)\n",
    "                self.Y[i].append(b)\n",
    "        self.axes[0].cla()\n",
    "        for x, y, fmt in zip(self.X, self.Y, self.fmts):\n",
    "            self.axes[0].plot(x, y, fmt)\n",
    "        self.config_axes()\n",
    "        display.display(self.fig)\n",
    "        display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91290f6c-081c-430f-8563-73166defe322",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "训练函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "500cf101-f3cb-44c5-abc6-bbfb770e7953",
   "metadata": {
    "origin_pos": 44,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):  \n",
    "    \"\"\"训练模型（定义见第3章）\"\"\"\n",
    "    animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],\n",
    "                        legend=['train loss', 'train acc', 'test acc'])\n",
    "    for epoch in range(num_epochs):\n",
    "        train_metrics = train_epoch_ch3(net, train_iter, loss, updater)\n",
    "        test_acc = evaluate_accuracy(net, test_iter)\n",
    "        animator.add(epoch + 1, train_metrics + (test_acc,))\n",
    "    train_loss, train_acc = train_metrics\n",
    "    assert train_loss < 0.5, train_loss\n",
    "    assert train_acc <= 1 and train_acc > 0.7, train_acc\n",
    "    assert test_acc <= 1 and test_acc > 0.7, test_acc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09e83970-88ed-4d77-a10a-92fad6a89449",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "小批量随机梯度下降来优化模型的损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "ed05114c-e815-44c4-bcce-10880f11286a",
   "metadata": {
    "origin_pos": 46,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "lr = 0.1\n",
    "\n",
    "def updater(batch_size):\n",
    "    return d2l.sgd([W, b], lr, batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e153647-c2d1-4497-a261-42dfc29ccfd9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "训练模型10个迭代周期"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "cc4149fd-a083-4a50-a164-d71513ea5edb",
   "metadata": {
    "origin_pos": 49,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
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     "metadata": {},
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   ],
   "source": [
    "num_epochs = 10\n",
    "train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ec84ab6-8482-46a9-ab68-522f2faba21c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "对图像进行分类预测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f5909439-a31c-4ade-aab8-5bb3edb9fa23",
   "metadata": {
    "origin_pos": 51,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
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      "text/plain": [
       "<Figure size 1200x150 with 8 Axes>"
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   ],
   "source": [
    "def predict_ch3(net, test_iter, n=8):  \n",
    "    \"\"\"预测标签（定义见第3章）\"\"\"\n",
    "    for X, y in test_iter:\n",
    "        break\n",
    "    trues = d2l.get_fashion_mnist_labels(y)\n",
    "    preds = d2l.get_fashion_mnist_labels(net(X).argmax(axis=1))\n",
    "    titles = [true +'\\n' + pred for true, pred in zip(trues, preds)]\n",
    "    d2l.show_images(\n",
    "        X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n])\n",
    "\n",
    "predict_ch3(net, test_iter)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb05ae93-ca43-4978-b77b-cca182c45c8f",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": []
   },
   "source": [
    "## softmax回归的简洁实现"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7da7eb8-6bad-4d17-83a7-24ec09779ef0",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "通过深度学习框架的高级API能够使实现softmax回归变得更加容易"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "b598a5ff-1618-4bc3-a8aa-c627a3d3caa7",
   "metadata": {
    "origin_pos": 4,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "from d2l import torch as d2l\n",
    "\n",
    "batch_size = 256\n",
    "train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd341874-7652-4afe-aa0a-41207311318f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Softmax回归的输出层是一个全连接层"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "ee566c3d-2669-4149-bdcb-d9832ed4c4d5",
   "metadata": {
    "origin_pos": 7,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "# PyTorch不会隐式地调整输入的形状。因此，\n",
    "# 我们在线性层前定义了展平层（flatten），来调整网络输入的形状\n",
    "net = nn.Sequential(nn.Flatten(), nn.Linear(784, 10))\n",
    "\n",
    "def init_weights(m):\n",
    "    if type(m) == nn.Linear:\n",
    "        nn.init.normal_(m.weight, std=0.01)\n",
    "\n",
    "net.apply(init_weights);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1330ec1d-3c66-46a0-8422-948553a33c41",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "在交叉熵损失函数中传递未规范化的预测，并同时计算softmax及其对数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "fcac843e-7436-4e88-bdf3-480bdfa12f26",
   "metadata": {
    "origin_pos": 11,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "loss = nn.CrossEntropyLoss(reduction='none')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c7344bf-3aa5-4a19-8b25-b0296f9e238d",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "使用学习率为0.1的小批量随机梯度下降作为优化算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "3c5df7de-6a41-4069-bab3-3b518da1f30f",
   "metadata": {
    "origin_pos": 15,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "trainer = torch.optim.SGD(net.parameters(), lr=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eef015d8-1fbc-4dd1-b1c0-5bbb46ec6d34",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "调用\n",
    "之前\n",
    "定义的训练函数来训练模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "2b28c827-05cd-4c4b-9dd7-db27d8067a27",
   "metadata": {
    "origin_pos": 18,
    "tab": [
     "pytorch"
    ],
    "tags": []
   },
   "outputs": [
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   "source": [
    "num_epochs = 10\n",
    "d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)"
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